model of saturating synaptic transmission

[shyam_u2]

Hello Ted,

With reference to this mechanism in Model DB,

https://senselab.med.yale.edu/modeldb/S ... ynapse.mod

Given a Synaptic current waveform Isyn(t) say for AMPA synapse, How do I compute the forward and backward rate constants (r1 and 1/tau2 ) of this mechanism. For exp2syn.mod you would do this by dividing the waveform by (V-Erev) and fitting the resulting waveform to A*(exp(-k1*t) - exp(-k2*t)) and use k1 and k2 as parameters for exp2syn mechanism. But I am bit confused how to do for this mechanism.

Thanks in advance.

[ted]

I can see why you're confused. This is a model of satuating synaptic transmission--for relevant publications see model entry 18198 in ModelDB and these articles:
Destexhe A, Mainen ZF, Sejnowski TJ (1994) Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism. J Comput Neurosci 1:195-230
Destexhe A, Mainen Z, Sejnowski TJ (1994) An efficient method for computing synaptic conductances based on a kinetic model of receptor binding Neural Comput 6:14-18

However, the source code is written in a way that is a bit obscure. Also the units of several parameters are incorrect (but not in a way that causes the mechanism to give incorrect results). Furthermore, this particular model has a serious limitation: it can only handle a single event stream. Its maximum synaptic conductance is controlled by the gmax parameter, and it ignores the weight associated with the event stream's NetCon. Consequently it is not an efficient mechanism to use to represent situations in which two or more synapses are attached to the same compartment--you'll need a separate instance of this point process to represent each synapse. Finally, the very name of the gmax parameter is misleading, because it doesn't actually specify the maximum conductance that the synapse would generate if the synapse is tonically activated (i.e. the condition of "maximal temporal summation" caused by rapid repetitive presynaptic spiking). Code for a much more capable saturating synapse called AMPA_S is presented as example 10.6 in the NEURON Book--it handles temporal summation of multiple convergent streams with different weights, and each NetCon's weight specifies the actual maximum conductance that would be produced by tonic activation of that afferent "axon." There's also a very similar ampa.mod that you get when you install NEURON--it's in
nrn/examples/nrniv/netcon/ampa.mod

Saturating synaptic transmission mechanisms are most useful when the exact synaptic conductance time course produced by each individual presynaptic spike is less important than the fact that saturation* prevents high frequency presynaptic spiking from producing unrealistically large temporal summation of the postsynaptic conductance change.
*--saturation happens because there is only a limited number of ligand-gated channels in the postsynaptic terminal

The basic idea behind saturating synaptic transmission mechanisms is very simple, and I will explain it using a much clearer notation that what is used in Synapse.mod.

Assume a synapse whose channels can exist in two states: closed and open.
Transmitter binds to receptors on the closed channels through a first order reaction with forward and reverse rate constants f and r. Also assume that when transmitter is present, its concentration is sufficient to completely saturate the receptors if it stays in the cleft for a long enough time (this is called the "large excess" assumption). Then we have a mechanism that is described by this kinetic scheme

Code: Select all

        f
T + C <-> O
      r

where C and O are the fractions of channels that are closed or open, respectively (so C+O = 1), and T is a parameter that has the value 1 or 0 to indicate the presence or absence of neurotransmitter in the synaptic cleft. We can immediately write the ODE that governs the time course of O:
dO/dt = f*T*C - r*O

When the presynaptic terminal has been silent for a long time, T=0 and
dO/dt = -r*O
When the presynaptic terminal spikes, T becomes 1 for a fixed time interval, and during that interval the ODE is

Code: Select all

dO/dt = f*T*C - r*O
      = f*(1 - O) - r*O
      = f - (f + r)*O

Define tau = 1/(f + r).
dO/dt = f - O/tau
Define Oinf = f*tau
dO/dt = (Oinf - O)/tau

Now you see that the time course of O is completely monoexponential with time constant tau = 1/(f+r). The only difference between "transmitter present" and "transmitter absent" conditions is the value of Oinf: 0 when T=0 and f/(f+r) when T=1.

[shyam_u2]

That was very explanative indeed! Thank you.

So when the transmitter is present, time course of O is governed by 1/f+r and when T=0 (transmitter absent) it is governed by 1/r (dO/dt = -O*r). So if have a synaptic conductance waveform, I fit a mono exponential curve separately to rise regime with time constant tau1 and a similar one to decay regime ( time constant tau2) and make sure that tau1 = (1/f+r) and tau2 = 1/r to make sure that the time course of synaptic current is the same as in experiment.
Am I correct here ?

Thank you.

[ted]

dO/dt = (Oinf - O)/tau
under all conditions. The time constant tau is always 1/(f+r) regardless of whether O is increasing or decreasing. The only difference between "transmitter present" and "transmitter absent" conditions is the value of Oinf, i.e. the "steady state" value toward which O moves.